nx_fnet_train_gate.nx

nx_fnet_train_gate.nx -- GATE for FNET-003: the trainable FNet block (arc convergence). Proves, by RUNNING: G1 f32 FFT correctness: the f32 radix-2 FFT equals the naive O(n^2) f32 DFT (same CORDIC->f32 twiddles) at n=8 -- the f32 transform is a real Fourier transform. G2 FNet-op GRADCHECK through the autograd: x[4,4] -> ta_fnet -> mse(.,target); analytic gradient (the self-adjoint backward, dx = fnet_mix(dL/dy)) vs central finite difference per input cell (h=1/128, rel<1/32 floor 1/64). Proves the sub-quadratic mixer is now a correctly-differentiable tape op. G3 TRAIN through the op: gradient descent on the input to minimize mse(fnet(x), target) -- the loss strictly decreases, so gradients flow end-to-end through the FNet block. Evidence -> knowledge/status/fnet_train.log (FNETTRAINGATE authored=organ ... verdict=GREEN). license_tier: ORIGINAL